1. A SPEECH, consisting of three propositions, from two of which the third follows, is called a SYLLOGISM; and that which follows is called the conclusion; the other two premises. For example, this speech, every man is a living creature, every living creature is a body, therefore, every man is a body, is a syllogism, because the third proposition follows from the two first; that is, if those be granted to be true, this must also be granted to be true.

2. From two propositions which have not one term common, no conclusion can follow; and therefore no syllogism can be made of them. For let any two premises, a man is a living creature, a tree is a plant, be both of them true, yet because it cannot be collected from them that plant is the name of a man, or man the name of a plant, it is not necessary that this conclusion, a man is a plant, should be true. Corollary: therefore, in the premises of a syllogism there can be but three terms.

Besides, there can be no term in the conclusion, which was not in the premises. For let any two premises be, a man is a living creature, a living creature is a body, yet if any other term be put in the conclusion, as man is two-footed; though it be true, it cannot follow from the premises, because from them it cannot be collected, that the name two-footed belongs to a man; and therefore, again, in every syllogism there can be but three terms.

3. Of these terms, that which is the predicate in the conclusion, is commonly called the major; that which is the subject in the conclusion, the minor, and the other is the middle term; as in this syllogism, a man is a living creature, a living creature is a body, therefore, a man is a body, body is the major, man the minor, and living creature the middle term. Also of the premises, that in which the major term is found, is called the major proposition, and that which has the minor term, the minor proposition.

4. If the middle term be not in both the premises determined to one and the same singular thing, no conclusion will follow, nor syllogism be made. For let the minor term be man, the middle term living creature, and the major term lion; and let the premises be, man is a living creature, some living creature is a lion, yet it will not follow that every or any man is a lion. By which it is manifest, that in every syllogism, that proposition which has the middle term for its subject, ought to be either universal or singular, but not particular nor indefinite. For example, this syllogism, every man is a living creature, some living creature is four-footed, therefore some man is four-footed, is therefore faulty, because the middle term, living creature, is in the first of the premises determined only to man, for there the name of living creature is given to man only, but in the latter premise it may be understood of some other living creature besides man. But if the latter premise had been universal, as here, every man is a living creature, every living creature is a body, therefore every man is a body, the syllogism had been true; for it would have followed that body had been the name of every living creature, that is of man; that is to say, the conclusion every man is a body had been true. Likewise, when the middle term is a singular name, a syllogism may be made, I say a true syllogism, though useless in philosophy, as this, some man is Socrates, Socrates is a philosopher, therefore, some man is a philosopher; for the premises being granted, the conclusion cannot be denied.

5. And therefore of two premises, in both which the middle term is particular, a syllogism cannot be made; for whether the middle term be the subject in both the premises, or the predicate in both, or the subject in one, and the predicate in the other, it will not be necessarily determined to the same thing. For let the premises be,

Some man is blind,		In both which the middle
Some man is learned,		term is the subject,

it will not follow that blind is the name of any learned man, or learned the name of any blind man, seeing the name learned does not contain the name blind, nor this that; and therefore it is not necessary that both should be names of the same man. So from these premises,

Every man is a living-creature,		In both which the middle
Every horse is a living-creature,		term is the predicate,

nothing will follow. For seeing living creature is in both of them indefinite, which is equivalent to particular, and that man may be one kind of living creature, and horse another kind, it is not necessary that man should be the name of horse, or horse of man. Or if the premises be,

Every man is a living-creature, Some living creature is four-footed,		In one of which the middle-term
		is the subject, and in the
		other the predicate,

the conclusion will not follow, because the name living creature being not determined, it may in one of them be understood of man, in the other of not-man.

6. Now it is manifest from what has been said, that a syllogism is nothing but a collection of the sum of two propositions, joined together by a common term, which is called the middle term. And as proposition is the addition of two names, so syllogism is the adding together of three.

7. Syllogisms are usually distinguished according to their diversity of figures, that is, by the diverse position of the middle term. And again in figure there is a distinction of certain moods, which consist of the differences of propositions in quantity and quality. The first figure is that, in which the terms are placed one after another according to their latitude of signification; in which order the minor term is first, the middle term next, and the major last; as, if the minor term be man, the middle term, living creature, and the major term, body, then, man is a living-creature, is a body, will be a syllogism in the first figure: in which, man is a living creature is the minor proposition; the major, living creature is a body, and the conclusion, or sum of both, man is a body. Now this figure is called direct, because the terms stand in direct order; and it is varied by quantity and quality into four moods: of which the first is that wherein all the terms are positive, and the minor term universal, as every man is a living creature, every living creature is a body: in which all the propositions are affirmative, and universal. But if the major term be a negative name, and the minor an universal name, the figure will be in the second mood, as, every man is a living creature, every living creature is not a tree, in which the major proposition and conclusion are both universal and negative. To these two, are commonly added two more, by making the minor term particular. Also it may happen that both the major and middle terms are negative terms, and then there arises another mood, in which all the propositions are negative, and yet the syllogism will be good; as, if the minor term be man, the middle term not a stone, and the major term not a flint, this syllogism, no man is a stone, whatsoever is not a stone is not a flint, therefore, no man is a flint, is true, though it consist of three negatives. But in philosophy, the profession whereof is to establish universal rules concerning the properties of things, seeing the difference betwixt negatives and affirmatives is only this, that in the former the subject is affirmed by a negative name, and by a positive in the latter, it is superfluous to consider any other mood in direct figure, besides that, in which all the propositions are both universal and affirmative.

8. The thoughts in the mind answering to a direct syllogism, proceed in this manner; first, there is conceived a phantasm of the thing named, with that accident or quality thereof, for which it is in the minor proposition called by that name which is the subject; next, the mind has a phantasm of the same thing with that accident, or quality, for which it hath the name, that in the same proposition is the predicate; thirdly, the thought returns of the same thing as having that accident in it, for which it is called by the name, that is the predicate of the major proposition; and lastly, remembering that all those are the accidents of one and the same thing, it concludes that those three names are also names of one and the same thing; that is to say, the conclusion is true. For example, when this syllogism is made, man is a living creature, a living creature is a body, therefore, man is a body, the mind conceives first an image of a man speaking or discoursing, and remembers that that, which so appears, is called man; then it has the image of the same man moving, and remembers that that, which appears so, is called living creature; thirdly, it conceives an image of the same man, as filling some place or space, and remembers that what appears so is called body; and lastly, when it remembers that that thing, which was extended, and moved and spake, was one and the same thing, it concludes that the three names, man, living creature, and body, are names of the same thing, and that therefore man is a living creature is a true proposition. From whence it is manifest, that living creatures that have not the use of speech, have no conception or thought in the mind, answering to a syllogism made of universal propositions; seeing it is necessary to think not only of the thing, but also by turns to remember the divers names, which for divers considerations thereof are applied to the same.

9. The rest of the figures arise either from the inflexion, or inversion of the first or direct figure; which is done by changing the major, or minor, or both the propositions, into converted propositions equipollent to them.

From whence follow three other figures; of which, two are inflected, and the third inverted. The first of these three is made by the conversion of the major proposition. For let the minor, middle, and major terms stand in direct order, thus, man is a living creature, is not a stone, which is the first or direct figure; the inflection will be by converting the major proposition in this manner, man is a living creature, a stone is not a living creature; and this is the second figure, or the first of the indirect figures; in which the conclusion will be, man is not a stone. For (having shown in the last chapter, art. 14, that universal propositions, converted by contradiction of the terms, are equipollent) both those syllogisms conclude alike; so that if the major be read (like Hebrew) backwards, thus, a living creature is not a stone, it will be direct again, as it was before. In like manner this direct syllogism, man is not a tree, is not a pear-tree, will be made indirect by converting the major proposition (by contradiction of the terms) into another equipollent to it, thus, man is not a tree, a pear-tree is a tree; for the same conclusion will follow, man is not a pear-tree.

But for the conversion of the direct figure into the first indirect figure, the major term in the direct figure ought to be negative. For though this direct, man is a living creature, is a body, be made indirect, by converting the major proposition, thus,

Yet this conversion appears so obscure, that this mood is of no use at all. By the conversion of the major proposition, it is manifest, that in this figure, the middle term is always the predicate in both the premises.

10. The second indirect figure is made by converting the minor proposition, so as that the middle term is the subject in both. But this never concludes universally, and therefore is of no use in philosophy. Nevertheless I will set down an example of it; by which this direct

by conversion of the minor proposition, will stand thus,

For every man isman is a living creature cannot be converted into this, every living creature is a man: and therefore if this syllogism be restored to its direct form, the minor proposition will be some man is a living creature, and consequently the conclusion will be some man is a body, seeing the minor term man, which is the subject in the conclusion, is a particular name.

11. The third indirect or inverted figure, is made by the conversion of both the premises. For example, this direct syllogism,

being inverted, will stand thus,

which conclusion is the converse of the direct conclusion, and equipollent to the same.

The figures, therefore, of syllogisms, if they be numbered by the diverse situation of the middle term only, are but three; in the first whereof, the middle term has the middle place; in the second, the last; and in the third, the first place. But if they be numbered according to the situation of the terms simply, they are four; for the first may be distinguished again into two, namely, into direct and inverted. From whence it is evident, that the controversy among logicians concerning the fourth figure, is a mere λογόμαχια, or contention about the name thereof; for, as for the thing itself, it is plain that the situation of the terms (not considering the quantity or quality by which the moods are distinguished) makes four differences of syllogisms, which may be called figures, or have any other name at pleasure.

12. In every one of these figures there are many moods, which are made by varying the premises according to all the differences they are capable of, by quantity and quality; as namely, in the direct figure there are six moods; in the first indirect figure, four; in the second, fourteen; and in the third, eighteen. But because from the direct figure I rejected as superfluous all moods besides that which consists of universal propositions, and whose minor proposition is affirmative, I do, together with it, reject the moods of the rest of the figures which are made by conversion of the premises in the direct figure.

13. As it was showed before, that in necessary propositions a categorical and hypothetical proposition are equipollent; so likewise it is manifest that a categorical and hypothetical syllogism are equivalent. For every categorical syllogism, as this,

is of equal force with this hypothetical syllogism:

In like manner, this categorical syllogism in an indirect figure,

is equivalent to this hypothetical syllogism:

And thus much seems sufficient for the nature of syllogisms; (for the doctrine of moods and figures is clearly delivered by others that have written largely and profitably of the same). Nor are precepts so necessary as practice for the attaining of true ratiocination; and they that study the demonstrations of mathematicians, will sooner learn true logic, than they that spend time in reading the rules of syllogizing which logicians have made; no otherwise than little children learn to go, not by precepts, but by exercising their feet. This, therefore, may serve for the first pace in the way to Philosophy.

In the next place I shall speak of the faults and errors into which men that reason unwarily are apt to fall; and of their kinds and causes.

CHAPTER V.

OF ERRING, FALSITY, AND CAPTIONS.

1. Erring and falsity how they differ. Error of the mind by itself without the use of words, how it happens.—2. A sevenfold incoherency of names, every one of which makes always a false proposition.—3. Examples of the first manner of incoherency.—4. Of the second.—5. Of the third.—6. Of the fourth.—7. Of the fifth.—8. Of the sixth.—9. Of the seventh.—10. Falsity of propositions detected by resolving the terms with definitions continued till they come to simple names, or names that are the most general of their kind.—11. Of the fault of a syllogism consisting in the implication of the terms with the copula.—12. Of the fault which consists in equivocation.—13. Sophistical captions are oftener faulty in the matter than in the form of syllogisms.

1. Men are subject to err not only in affirming and denying, but also in perception, and in silent cogitation. In affirming and denying, when they call any thing by a name, which is not the name thereof; as if from seeing the sun first by reflection in water, and afterwards again directly in the firmament, we should to both those appearances give the name of sun, and say there are two suns; which none but men can do, for no other living creatures have the use of names. This kind of error only deserves the name of falsity, as arising, not from sense, nor from the things themselves, but from pronouncing rashly; for names have their constitution, not from the species of things, but from the will and consent of men. And hence it comes to pass, that men pronounce falsely, by their own negligence, in departing from such appellations of things as are agreed upon, and are not deceived neither by the things, nor by the sense; for they do not perceive that the thing they see is called sun, but they give it that name from their own will and agreement. Tacit errors, or the errors of sense and cogitation, are made, by passing from one imagination to the imagination of another different thing; or by feigning that to be past, or future, which never was, nor ever shall be; as when, by seeing the image of the sun in water, we imagine the sun itself to be there; or by seeing swords, that there has been or shall be fighting, because it uses to be so for the most part; or when from promises we feign the mind of the promiser to be such and such; or lastly, when from any sign we vainly imagine something to be signified, which is not. And errors of this sort are common to all things that have sense; and yet the deception proceeds neither from our senses, nor from the things we perceive; but from ourselves while we feign such things as are but mere images to be something more than images. But neither things, nor imaginations of things, can be said to be false, seeing they are truly what they are; nor do they, as signs, promise any thing which they do not perform; for they indeed do not promise at all, but we from them; nor do the clouds, but we, from seeing the clouds, say it shall rain. The best way, therefore, to free ourselves from such errors as arise from natural signs, is first of all, before we begin to reason concerning such conjectural things, to suppose ourselves ignorant, and then to make use of our ratiocination; for these errors proceed from the want of ratiocination; whereas, errors which consist in affirmation and negation, (that is, the falsity of propositions) proceed only from reasoning amiss. Of these, therefore, as repugnant to philosophy, I will speak principally.

2. Errors which happen in reasoning, that is, in syllogizing, consist either in the falsity of the premises, or of the inference. In the first of these cases, a syllogism is said to be faulty in the matter of it; and in the second case, in the form. I will first consider the matter, namely, how many ways a proposition may be false; and next the form, and how it comes to pass, that when the premises are true, the inference is, notwithstanding, false.

Seeing, therefore, that proposition only is true, (chap, III, art. 7) in which are copulated two names of one and the same thing; and that always false, in which names of different things are copulated, look how many ways names of different things may be copulated, and so many ways a false proposition may be made.

Now, all things to which we give names, may be reduced to these four kinds, namely, bodies, accidents, phantasms, and names themselves; and therefore, in every true proposition, it is necessary that the names copulated, be both of them names of bodies, or both names of accidents, or both names of phantasms, or both names of names. For names otherwise copulated are incoherent, and constitute a false proposition. It may happen, also, that the name of a body, of an accident, or of a phantasm, may be copulated with the name of a speech. So that copulated names may be incoherent seven manner of ways.

1. If the name of a Body				the name of an Accident.
2. If the name of a Body				the name of a Phantasm.
3. If the name of a Body		be		the name of a Name.
4. If the name of an Accident		copulated		the name of a Phantasm.
5. If the name of an Accident		with		the name of a Name.
6. If the name of a Phantasm				the name of a Name.
7. If the name of a Body,				the name of a Speech.
Accident, or Phantasm

Of all which I will give some examples.

3. After the first of these ways propositions are false, when abstract names are copulated with concrete names; as (in Latin and Greek) esse est ens, essentia est ens, τὸ τί ἦν ειναὶ (i.); quidditas est ens, and many the like, which are found in Aristotle's Metaphysics. Also, the understanding worketh, the understanding understandeth, the sight seeth; a body is magnitude, a body is quantity, a body is extension; to be a man is a man, whiteness is a white thing, &c.; which is as if one should say, the runner is the running, or the walk walketh. Moreover, essence is separated, substance is abstracted: and others like these, or derived from these, (with which common philosophy abounds.) For seeing no subject of an accident (that is, no body) is an accident: no name of an accident ought to be given to a body, nor of a body to an accident.

4. False, in the second manner, are such propositions as these; a ghost is a body, or a spirit, that is, a thin body; sensible species fly up and down in the air, or are moved hither and thither, which is proper to bodies; also, a shadow is moved, or is a body; light is moved, or is a body; colour is the object of sight, sound of hearing; space or place is extended; and innumerable others of this kind. For seeing ghosts, sensible species, a shadow, light, colour, sound, space, &c. appear to us no less sleeping than waking, they cannot be things without us, but only phantasms of the mind that imagines them; and therefore the names of these, copulated with the names of bodies, cannot constitute a true proposition.

5. False propositions of the third kind, are such as these; genus est ens, universale est ens, ens de ente prædicatur. For genus, and universale, and predicare, are names of names, and not of things. Also, number is infinite, is a false proposition; for no number can be infinite, but only the word number is then called an indefinite name when there is no determined number answering to it in the mind.

6. To the fourth kind belong such false propositions as these, an object is of such magnitude or figure as appears to the beholders; colour, light, sound, are in the object; and the like. For the same object appears sometimes greater, sometimes lesser, sometimes square, sometimes round, according to the diversity of the distance and medium; but the true magnitude and figure of the thing seen is always one and the same; so that the magnitude and figure which appears, is not the true magnitude and figure of the object, nor anything but phantasm; and therefore, in such propositions as these, the names of accidents are copulated with the names of phantasms.

7. Propositions are false in the fifth manner, when it is said that the definition is the essence of a thing; whiteness, or some other accident, is the genus, or universal. For definition is not the essence of any thing, but a speech signifying what we conceive of the essence thereof; and so also not whiteness itself, but the word whiteness, is a genus, or an universal name.

8. In the sixth manner they err, that say the idea of anything is universal; as if there could be in the mind an image of a man, which were not the image of some one man, but a man simply, which is impossible; for every idea is one, and of one thing; but they are deceived in this, that they put the name of the thing for the idea thereof.

9. They err in the seventh manner, that make this distinction between things that have being, that some of them exist by themselves, others by accident; namely, because Socrates is a man is a necessary proposition, and Socrates is a musician a contingent proposition, therefore they say some things exist necessarily or by themselves, others contingently or by accident; whereby, seeing necessary, contingent, by itself, by accident, are not names of things, but of propositions, they that say any thing that has being, exists by accident, copulate the name of a proposition with the name of a thing. In the same manner also, they err, which place some ideas in the understanding, others in the fancy; as if from the understanding of this proposition, man is a living creature, we had one idea or image of a man derived from sense to the memory, and another to the understanding; wherein that which deceives them is this, that they think one idea should be answerable to a name, another to a proposition, which is false; for proposition signifies only the order of those things one after another, which we observe in the same idea of man; so that this proposition, man is a living creature raises but one idea in us, though in that idea we consider that first, for which he is called man, and next that, for which he is called living creature. The falsities of propositions in all these several manners, is to be discovered by the definitions of the copulated names.

10. But when names of bodies are copulated with names of bodies, names of accidents with names of accidents, names of names with names of names, and names of phantasms, with names of phantasms, if we, nevertheless, remain still doubtful whether such propositions are true, we ought then in the first place to find out the definition of both those names, and again the definitions of such names as are in the former definition, and so proceed by a continual resolution till we come to a simple name, that is, to the most general or most universal name of that kind; and if after all this, the truth or falsity thereof be not evident, we must search it out by philosophy, and ratiocination, beginning from definitions. For every proposition, universally true, is either a definition, or part of a definition, or the evidence of it depends upon definitions.

11. That fault of a syllogism which lies hid in the form thereof, will always be found either in the implication of the copula with one of the terms, or in the equivocation of some word; and in either of these ways there will be four terms, which (as I have shewn) cannot stand in a true syllogism. Now the implication of the copula with either term, is easily detected by reducing the propositions to plain and clear predication; as (for example) if any man should argue thus,

the fallacy will easily appear by reducing it, thus:

where there are manifestly these four terms, the hand, touching the pen, the pen, and touching the the paper. But the danger of being deceived by sophisms of this kind, does not seem to be so great, as that I need insist longer upon them.

12. And though there may be fallacy in equivocal terms, yet in those that be manifestly such, there is none at all; nor in metaphors, for they profess the transferring of names from one thing to another. Nevertheless, sometimes equivocals (and those not very obscure) may deceive; as in this argumentation:--It belongs to metaphysics to treat of principles; but the first principle of all, is, that the same thing cannot both exist and not exist at the same time; and therefore it belongs to metaphysics to treat whether the same thing may both exist and not exist at the same time; where the fallacy lies in the equivocation of the word principle; for whereas Aristotle in the beginning of his Metaphysics, says, that the treating of principles belongs to primary science, he understands by principles, causes of things, and certain existences which he calls primary; but where he says a primary proposition is a principle, by principle, there, he means the beginning and cause of knowledge, that is, the understanding of words, which, if any man want, he is incapable of learning.

13. But the captions of sophists and sceptics, by which they were wont, of old, to deride and oppose truth, were faulty for the most part, not in the form, but in the matter of syllogism; and they deceived not others oftener than they were themselves deceived. For the force of that famous argument of Zeno against motion, consisted in this proposition, whatsoever may be divided into parts, infinite in number, the same is infinite; which he, without doubt, thought to be true, yet nevertheless is false. For to be divided into infinite parts, is nothing else but to be divided into as many parts as any man will. But it is not necessary that a line should have parts infinite in number, or be infinite, because I can divide and subdivide it as often as I please; for how many parts soever I make, yet their number is finite; but because he that says parts, simply, without adding how many, does not limit any number, but leaves it to the determination of the hearer, therefore we say commonly, a line may be divided infinitely; which cannot be true in any other sense.

And thus much may suffice concerning syllogism, which is, as it were, the first pace towards philosophy; in which I have said as much as is necessary to teach any man from whence all true argumentation has its force. And to enlarge this treatise with all that may be heaped together, would be as superfluous, as if one should (as I said before) give a young child precepts for the teaching of him to go; for the art of reasoning is not so well learned by precepts as by practice, and by the reading of those books in which the conclusions are all made by severe demonstration. And so I pass on to the way of philosophy, that is, to the method of study.

CHAPTER VI.

OF METHOD.

1. Method and science defined.—2. It is more easily known concerning singular, than universal things, that they are; and contrarily, it is more easily known concerning universal, than singular things, why they are, or what are their causes.—3. What it is philosophers seek to know.—4. The first part, by which principles are found out, is purely analytical.—5. The highest causes, and most universal in every kind, are known by themselves.—6. Method from principles found out, tending to science simply, what it is.—7. That method of civil and natural science, which proceeds from sense to principles, is analytical; and again, that, which begins at principles, is synthetical.—8. The method of searching out, whether any thing propounded be matter or accident.—9. The method of seeking whether any accident be in this, or in that subject.—10. The method of searching after the cause of any effect propounded.—11. Words serve to invention, as marks; to demonstration, as signs.—12. The method of demonstration is synthetical.—13. Definitions only are primary and universal propositions.—14. The nature and definition of a definition.—15. The properties of a definition.—16. The nature of a demonstration.—17. The properties of a demonstration, and order of things to be demonstrated.—18. The faults of a demonstration.—19. Why the analytical method of geometricians cannot be treated of in this place.